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A FAS approach for stabilization of generalized chained forms: part 2. Continuous control laws

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Science China(Information Sciences) 2024年第3期67卷 114-135页

作者： Guang-Ren DUAN Center for Control Theory and Guidance Technology Harbin Institute of Technology Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern University of Science and Technology

In this paper, continuous time-varying stabilizing controllers for the type of general nonholonomic systems proposed and treated in part 1 are designed using the fully actuated system(FAS) approach. The key step is to differentiate the first scalar equation, and by control of the obtained second-order scalar system, a proportional plus integral feedback form for the first control variable is obtained. With the solution to this designed second-order scalar system, the rest equations in the nonholonomic system form an independent time-varying subsystem which is then handled by the FAS approach. The overall designed controller contains an almost arbitrarily chosen design parameter, and is proven to guarantee the uniformly and globally exponential stability of the closed-loop system. The proposed approach is simple and effective,and is demonstrated with a practical example of ship control.

关键词： nonholonomic systems feedback stabilization fully actuated systems Lyapunov stability continuous controllers

feedback stabilization of N-dimensional stochastic quantum systems based on bang-bang control

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Control Theory and Technology 2017年第3期15卷 206-218页

作者： Xiaqing SUN Sen KUANG Yanan LIU Juan ZHOU Shuang CONG Department of Automation University of Science and Technology of China Hefei Anhui 230027 China

For an N-dimensional quantum system under the influence of continuous measurement, this paper presents a switching control scheme where the control law is of bang-bang type and achieves asymptotic preparation of an arbitrarily given eigenstate of a non-degenerate and degenerate measurement operator, respectively. In the switching control strategy, we divide the state space into two parts： a set containing a target state, and its complementary set. By analyzing the stability of the stochastic system model under consideration, we design a constant control law and give some conditions that the control Hamiltonian satisfies so that the system trajectories in the complementary set converge to the set which contains the target state. Further, for the case of a non-degenerate measurement operator, we show that the system trajectories in the set containing the target state will automatically converge to the target state via quantum continuous measurement theory; while for the case of a degenerate measurement operator, the corresponding system trajectories will also converge to the target state via the construction of the control Hamiltonians. The convergence of the whole closed-loop systems under the cases of a non-degenerate and a degenerate measurement operator is strictly proved. The effectiveness of the proposed switching control scheme is verified by the simulation experiments on a finite-dimensional angular momentum system and a two-qubit system.

关键词： Quantum systems feedback stabilization bang-bang control switching strategy

feedback stabilization for a Class of Second Order Singular Distributed Parameter System in Hilbert Space

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Acta Mathematicae Applicatae Sinica 2015年第1期31卷 89-100页

作者： Feng LIU Guo-dong SHI Zhao-qiang GE School of Mathematics and Physics Jiangsu University of Technology School of Information Science and Engineering Changzhou University Department of Applied Mathematics Xi’an Jiaotong University

feedback stabilization for a class of second order singular distributed parameter system with multi- inputs is discussed via functional analysis and operator theory in Hilbert space, the solutions of the problem and the constructive expressions of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the stability of the singular distributed parameter system.

关键词： feedback stabilization second order singular distributed parameter system multi-inputs Hilbert space

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stabilization via Fully Actuated System Approach:A Case Study

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Journal of Systems Science & Complexity 2022年第3期35卷 731-747页

作者： DUAN Guang-Ren Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055China Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China

In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)approach.It is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin exponentially.Such a result brings about a generalization of Lyapunov asymptotical stability,which is termed as global exponential sub-stability.The region of attraction is allowed to be an unbounded open set of the initial values with closure containing the origin.This sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin exponentially.Based on this sub-stabilization result,globally asymptotically stabilizing controllers for the system can be provided in two general ways,one is through combination with existing globally stabilizing controllers,and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.

关键词： feedback stabilization fully actuated system approach nonlinear systems region of attraction singularity sets

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Brockett’s First Example: An FAS Approach Treatment

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Journal of Systems Science & Complexity 2022年第2期35卷 441-456页

In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)approach.Firstly,it is shown that the system can be exponentially substabilized by a smooth controller in the sense that,except those starting from initial values on the z0-axis of the initial value space,all trajectories of the designed system as well as the control signals decay to zero exponentially.Secondly,global stabilization is realized through a way of enabling the trajectories starting from initial values on the z0-axis also to go to the origin.The idea is to firstly move an initial point on the z0-axis away from the axis using a pre-controller,and then to take over by the designed exponentially sub-stabilizing controller.

关键词： Exponential sub-stabilization feedback stabilization fully actuated system approach region of attraction singularity sets

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State feedback stabilization of Nonlinear Stochastic Systems

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State Feedback Stabilization of Nonlinear Stochastic Systems

第二十六届中国控制会议

作者： Zhang Weihai1,2,Yan Zhiguo 1 1.School of Electronic Information and Control Engineering,Shandong Institute of Light Industry,Jinan 250353,P.R.China2.College of Information and Electrical Engineering,Shandong University of Science and Technology,Qingdao 266510,P.R.China

This paper studies the feedback stabilization of nonlinear affine stochastic systems,for which,sufficient conditions for the locally and globally asymptotic stabilization in probability are presented by means of Hamilton-Jacobi inequalities （HJIs）.As corollaries,some previous results are improved.One example is given to show the validity of the developed theory.

关键词： Asymptotic stability in probability Hamilton-Jacobi inequality feedback stabilization

BOUNDARY feedback stabilization OF WAVE EQUATION BY SATURATING CONTROL

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BOUNDARY FEEDBACK STABILIZATION OF WAVE EQUATION BY SATURATI...

1997年中国控制会议

作者： Wei-Tao ZHANG De-Xing FENG Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080

＜正＞The stabilization of wave equation by a nonlinear boundary feedback with saturating control is studied. It is shown that in terms of energy method, the energy associated with the solution of the corresponding cl... 详细信息

关键词： Wave equation feedback stabilization boundary control.

stabilization of LTI Systems over Finite-State Fading Channels

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Stabilization of LTI Systems over Finite-State Fading Channe...

第26届中国控制与决策会议

作者： Nan Xiao Yugang Niu Lihua Xie Key Laboratory of Advanced Control and Optimization for Chemical Process (East China University of Science and Technology) Ministry of Education EXQUISITUS Centre for E-CitySchool of Electrical and Electronic EngineeringNanyang Technological University

ISBN: (纸本)9781479937097

This paper considers the state feedback stabilization over finite-state fading channels, where the stochastic characteristic of time-varying fading channels is assumed to be driven by a finite-state random process. The finite-state process is used to represent different channel fading amplitudes and/or to model different configurations of the overall physical environment. Necessary and sufficient conditions are given for stabilization over finite-state Markov fading channels.In the case of finite-state i.i.d. fading channels, explicit network requirements for stabilization are presented for both single-input case and multi-input case. Our results cover some existing results as special cases.

关键词： feedback stabilization Finite-State Fading Channels Networked Control

Designing Stabilizing Controller for Linear Delay Systems

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Designing Stabilizing Controller for Linear Delay Systems

第40届中国控制会议

作者： Guang-Da Hu Department of Mathematics Shanghai University

feedback stabilization of linear delay systems is studied. When the unstable characteristic roots of open-loop system is far from the imaginary axis, the discretization of the system may result in a large error. In this case, it is difficult to seek a stabilizing control law with the optimization algorithm in the literature. In order to overcome the difficulty, a state equation with a parameter is presented. Then a sequence optimization method is provided to design a stabilizing controller. The method is an improved version of that in the literature. A numerical example is given to illustrate the effectiveness of the sequence optimization method.

关键词： linear delay systems feedback stabilization state equation with a parameter sequence optimization method